Duplicate object suffix (.nnn) to be put elsewhere (prefix maybe?)
When duplicating Cube, it will create Cube.001, there is no feature that i'm aware of to allow you to specify the desired duplicate name or convention.

It is possible to rename using the reference to the object after  duplication, because the duplicate becomes the active_object

# with one object selected.
bpy.ops.object.duplicate(linked=False, mode='DUMMY')
obj = bpy.context.scene.active_object
obj.name = desired_name


or a mass rename if that makes sense

for obj in bpy.data.objects:
    if obj.type == 'MESH':
       if '.' in obj.name:
          # assuming it only has one period in the name.
          basename, postfix = obj.name.split('.')
          obj.name = postfix + '.' + basename